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<div class="title">Umeyama.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment">// Copyright (C) 2009 Hauke Heibel &lt;hauke.heibel@gmail.com&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#ifndef EIGEN_UMEYAMA_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="preprocessor">#define EIGEN_UMEYAMA_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">// This file requires the user to include </span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">// * Eigen/Core</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">// * Eigen/LU </span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment">// * Eigen/SVD</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment">// * Eigen/Array</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#include &quot;./InternalHeaderCheck.h&quot;</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160; </div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160; </div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="preprocessor">#ifndef EIGEN_PARSED_BY_DOXYGEN</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160; </div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="comment">// These helpers are required since it allows to use mixed types as parameters</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment">// for the Umeyama. The problem with mixed parameters is that the return type</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="comment">// cannot trivially be deduced when float and double types are mixed.</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160; </div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="comment">// Compile time return type deduction for different MatrixBase types.</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="comment">// Different means here different alignment and parameters but the same underlying</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="comment">// real scalar type.</span></div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="keyword">template</span>&lt;<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> OtherMatrixType&gt;</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="keyword">struct </span>umeyama_transform_matrix_type</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;{</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;  <span class="keyword">enum</span> {</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;    MinRowsAtCompileTime = internal::min_size_prefer_dynamic(MatrixType::RowsAtCompileTime, OtherMatrixType::RowsAtCompileTime),</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160; </div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;    <span class="comment">// When possible we want to choose some small fixed size value since the result</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;    <span class="comment">// is likely to fit on the stack. So here, min_size_prefer_dynamic is not what we want.</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;    HomogeneousDimension = int(MinRowsAtCompileTime) == <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> ? <a class="code" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> : int(MinRowsAtCompileTime)+1</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;  };</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160; </div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;  <span class="keyword">typedef</span> Matrix&lt;typename traits&lt;MatrixType&gt;::Scalar,</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    HomogeneousDimension,</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;    HomogeneousDimension,</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;    <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13ad0e7f67d40bcde3d41c12849b16ce6ea">AutoAlign</a> | (traits&lt;MatrixType&gt;::Flags &amp; <a class="code" href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">RowMajorBit</a> ? <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">RowMajor</a> : <a class="code" href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">ColMajor</a>),</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    HomogeneousDimension,</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    HomogeneousDimension</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;  &gt; type;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;};</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160; </div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;}</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160; </div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160; </div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Derived, <span class="keyword">typename</span> OtherDerived&gt;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;<span class="keyword">typename</span> internal::umeyama_transform_matrix_type&lt;Derived, OtherDerived&gt;::type</div>
<div class="line"><a name="l00097"></a><span class="lineno"><a class="line" href="group__Geometry__Module.html#gab3f5a82a24490b936f8694cf8fef8e60">   97</a></span>&#160;<a class="code" href="group__Geometry__Module.html#gab3f5a82a24490b936f8694cf8fef8e60">umeyama</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;Derived&gt;</a>&amp; src, <span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase&lt;OtherDerived&gt;</a>&amp; dst, <span class="keywordtype">bool</span> with_scaling = <span class="keyword">true</span>)</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;{</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::umeyama_transform_matrix_type&lt;Derived, OtherDerived&gt;::type TransformationMatrixType;</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::traits&lt;TransformationMatrixType&gt;::Scalar Scalar;</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::Real</a> RealScalar;</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160; </div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;  EIGEN_STATIC_ASSERT(!<a class="code" href="structEigen_1_1NumTraits.html">NumTraits&lt;Scalar&gt;::IsComplex</a>, NUMERIC_TYPE_MUST_BE_REAL)</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;  EIGEN_STATIC_ASSERT((internal::is_same&lt;Scalar, <span class="keyword">typename</span> internal::traits&lt;OtherDerived&gt;::Scalar&gt;::value),</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160; </div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  <span class="keyword">enum</span> { Dimension = internal::min_size_prefer_dynamic(Derived::RowsAtCompileTime, OtherDerived::RowsAtCompileTime) };</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160; </div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;Scalar, Dimension, 1&gt;</a> VectorType;</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;  <span class="keyword">typedef</span> <a class="code" href="classEigen_1_1Matrix.html">Matrix&lt;Scalar, Dimension, Dimension&gt;</a> MatrixType;</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="classEigen_1_1Matrix.html">internal::plain_matrix_type_row_major&lt;Derived&gt;::type</a> RowMajorMatrixType;</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160; </div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> m = src.<a class="code" href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">rows</a>(); <span class="comment">// dimension</span></div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;  <span class="keyword">const</span> <a class="code" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> n = src.<a class="code" href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#a2d768a9877f5f69f49432d447b552bfe">cols</a>(); <span class="comment">// number of measurements</span></div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160; </div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;  <span class="comment">// required for demeaning ...</span></div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;  <span class="keyword">const</span> RealScalar one_over_n = RealScalar(1) / <span class="keyword">static_cast&lt;</span>RealScalar<span class="keyword">&gt;</span>(n);</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160; </div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;  <span class="comment">// computation of mean</span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;  <span class="keyword">const</span> VectorType src_mean = src.<a class="code" href="classEigen_1_1DenseBase.html#aa1cabd3404528fe8cec4bab43d74bffc">rowwise</a>().<a class="code" href="classEigen_1_1VectorwiseOp.html#a7030fc687c24d687ed7cd70733ba611c">sum</a>() * one_over_n;</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;  <span class="keyword">const</span> VectorType dst_mean = dst.<a class="code" href="classEigen_1_1DenseBase.html#aa1cabd3404528fe8cec4bab43d74bffc">rowwise</a>().<a class="code" href="classEigen_1_1VectorwiseOp.html#a7030fc687c24d687ed7cd70733ba611c">sum</a>() * one_over_n;</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160; </div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;  <span class="comment">// demeaning of src and dst points</span></div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;  <span class="keyword">const</span> RowMajorMatrixType src_demean = src.<a class="code" href="classEigen_1_1DenseBase.html#a58837c81de446efbdb58da07b73a63c1">colwise</a>() - src_mean;</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;  <span class="keyword">const</span> RowMajorMatrixType dst_demean = dst.<a class="code" href="classEigen_1_1DenseBase.html#a58837c81de446efbdb58da07b73a63c1">colwise</a>() - dst_mean;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160; </div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;  <span class="comment">// Eq. (38)</span></div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;  <span class="keyword">const</span> MatrixType sigma = one_over_n * dst_demean * src_demean.transpose();</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160; </div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;  <a class="code" href="classEigen_1_1JacobiSVD.html">JacobiSVD&lt;MatrixType, ComputeFullU | ComputeFullV&gt;</a> svd(sigma);</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160; </div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;  <span class="comment">// Initialize the resulting transformation with an identity matrix...</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;  TransformationMatrixType Rt = TransformationMatrixType::Identity(m+1,m+1);</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160; </div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;  <span class="comment">// Eq. (39)</span></div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;  VectorType S = VectorType::Ones(m);</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160; </div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;  <span class="keywordflow">if</span>  ( svd.<a class="code" href="classEigen_1_1SVDBase.html#afc7fe1546b0f6e1801b86f22f5664cb8">matrixU</a>().<a class="code" href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061">determinant</a>() * svd.<a class="code" href="classEigen_1_1SVDBase.html#a245a453b5e7347f737295c23133238c4">matrixV</a>().<a class="code" href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061">determinant</a>() &lt; 0 )</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    S(m-1) = -1;</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160; </div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;  <span class="comment">// Eq. (40) and (43)</span></div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;  Rt.block(0,0,m,m).noalias() = svd.<a class="code" href="classEigen_1_1SVDBase.html#afc7fe1546b0f6e1801b86f22f5664cb8">matrixU</a>() * S.<a class="code" href="classEigen_1_1MatrixBase.html#a14235b62c90f93fe910070b4743782d0">asDiagonal</a>() * svd.<a class="code" href="classEigen_1_1SVDBase.html#a245a453b5e7347f737295c23133238c4">matrixV</a>().<a class="code" href="classEigen_1_1DenseBase.html#a43cbcd866a0737eb56642c2e992f0afd">transpose</a>();</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160; </div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;  <span class="keywordflow">if</span> (with_scaling)</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;  {</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;    <span class="comment">// Eq. (36)-(37)</span></div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;    <span class="keyword">const</span> Scalar src_var = src_demean.rowwise().squaredNorm().sum() * one_over_n;</div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160; </div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    <span class="comment">// Eq. (42)</span></div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    <span class="keyword">const</span> Scalar c = Scalar(1)/src_var * svd.<a class="code" href="classEigen_1_1SVDBase.html#a4e7bac123570c348f7ed6be909e1e474">singularValues</a>().dot(S);</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160; </div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;    <span class="comment">// Eq. (41)</span></div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;    Rt.col(m).head(m) = dst_mean;</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;    Rt.col(m).head(m).noalias() -= c*Rt.topLeftCorner(m,m)*src_mean;</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;    Rt.block(0,0,m,m) *= c;</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;  }</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;  {</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    Rt.col(m).head(m) = dst_mean;</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    Rt.col(m).head(m).noalias() -= Rt.topLeftCorner(m,m)*src_mean;</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;  }</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160; </div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;  <span class="keywordflow">return</span> Rt;</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;}</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160; </div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160; </div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// EIGEN_UMEYAMA_H</span></div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_a43cbcd866a0737eb56642c2e992f0afd"><div class="ttname"><a href="classEigen_1_1DenseBase.html#a43cbcd866a0737eb56642c2e992f0afd">Eigen::DenseBase::transpose</a></div><div class="ttdeci">TransposeReturnType transpose()</div><div class="ttdef"><b>Definition:</b> Transpose.h:184</div></div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_a58837c81de446efbdb58da07b73a63c1"><div class="ttname"><a href="classEigen_1_1DenseBase.html#a58837c81de446efbdb58da07b73a63c1">Eigen::DenseBase::colwise</a></div><div class="ttdeci">ConstColwiseReturnType colwise() const</div><div class="ttdef"><b>Definition:</b> DenseBase.h:551</div></div>
<div class="ttc" id="aclassEigen_1_1DenseBase_html_aa1cabd3404528fe8cec4bab43d74bffc"><div class="ttname"><a href="classEigen_1_1DenseBase.html#aa1cabd3404528fe8cec4bab43d74bffc">Eigen::DenseBase::rowwise</a></div><div class="ttdeci">ConstRowwiseReturnType rowwise() const</div><div class="ttdef"><b>Definition:</b> DenseBase.h:539</div></div>
<div class="ttc" id="aclassEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4_html_a2d768a9877f5f69f49432d447b552bfe"><div class="ttname"><a href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#a2d768a9877f5f69f49432d447b552bfe">Eigen::DenseCoeffsBase&lt; Derived, DirectWriteAccessors &gt;::cols</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index cols() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:65</div></div>
<div class="ttc" id="aclassEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4_html_ac22eb0695d00edd7d4a3b2d0a98b81c2"><div class="ttname"><a href="classEigen_1_1DenseCoeffsBase_3_01Derived_00_01DirectWriteAccessors_01_4.html#ac22eb0695d00edd7d4a3b2d0a98b81c2">Eigen::DenseCoeffsBase&lt; Derived, DirectWriteAccessors &gt;::rows</a></div><div class="ttdeci">EIGEN_CONSTEXPR Index rows() const EIGEN_NOEXCEPT</div><div class="ttdef"><b>Definition:</b> EigenBase.h:62</div></div>
<div class="ttc" id="aclassEigen_1_1JacobiSVD_html"><div class="ttname"><a href="classEigen_1_1JacobiSVD.html">Eigen::JacobiSVD</a></div><div class="ttdoc">Two-sided Jacobi SVD decomposition of a rectangular matrix.</div><div class="ttdef"><b>Definition:</b> JacobiSVD.h:514</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions.</div><div class="ttdef"><b>Definition:</b> MatrixBase.h:52</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_a14235b62c90f93fe910070b4743782d0"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a14235b62c90f93fe910070b4743782d0">Eigen::MatrixBase::asDiagonal</a></div><div class="ttdeci">const DiagonalWrapper&lt; const Derived &gt; asDiagonal() const</div><div class="ttdef"><b>Definition:</b> DiagonalMatrix.h:327</div></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html_a7ad8f77004bb956b603bb43fd2e3c061"><div class="ttname"><a href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061">Eigen::MatrixBase::determinant</a></div><div class="ttdeci">Scalar determinant() const</div><div class="ttdef"><b>Definition:</b> Determinant.h:110</div></div>
<div class="ttc" id="aclassEigen_1_1Matrix_html"><div class="ttname"><a href="classEigen_1_1Matrix.html">Eigen::Matrix</a></div><div class="ttdoc">The matrix class, also used for vectors and row-vectors.</div><div class="ttdef"><b>Definition:</b> Matrix.h:182</div></div>
<div class="ttc" id="aclassEigen_1_1SVDBase_html_a245a453b5e7347f737295c23133238c4"><div class="ttname"><a href="classEigen_1_1SVDBase.html#a245a453b5e7347f737295c23133238c4">Eigen::SVDBase::matrixV</a></div><div class="ttdeci">const MatrixVType &amp; matrixV() const</div><div class="ttdef"><b>Definition:</b> SVDBase.h:191</div></div>
<div class="ttc" id="aclassEigen_1_1SVDBase_html_a4e7bac123570c348f7ed6be909e1e474"><div class="ttname"><a href="classEigen_1_1SVDBase.html#a4e7bac123570c348f7ed6be909e1e474">Eigen::SVDBase::singularValues</a></div><div class="ttdeci">const SingularValuesType &amp; singularValues() const</div><div class="ttdef"><b>Definition:</b> SVDBase.h:203</div></div>
<div class="ttc" id="aclassEigen_1_1SVDBase_html_afc7fe1546b0f6e1801b86f22f5664cb8"><div class="ttname"><a href="classEigen_1_1SVDBase.html#afc7fe1546b0f6e1801b86f22f5664cb8">Eigen::SVDBase::matrixU</a></div><div class="ttdeci">const MatrixUType &amp; matrixU() const</div><div class="ttdef"><b>Definition:</b> SVDBase.h:175</div></div>
<div class="ttc" id="aclassEigen_1_1VectorwiseOp_html_a7030fc687c24d687ed7cd70733ba611c"><div class="ttname"><a href="classEigen_1_1VectorwiseOp.html#a7030fc687c24d687ed7cd70733ba611c">Eigen::VectorwiseOp::sum</a></div><div class="ttdeci">const SumReturnType sum() const</div><div class="ttdef"><b>Definition:</b> VectorwiseOp.h:480</div></div>
<div class="ttc" id="agroup__Geometry__Module_html_gab3f5a82a24490b936f8694cf8fef8e60"><div class="ttname"><a href="group__Geometry__Module.html#gab3f5a82a24490b936f8694cf8fef8e60">Eigen::umeyama</a></div><div class="ttdeci">internal::umeyama_transform_matrix_type&lt; Derived, OtherDerived &gt;::type umeyama(const MatrixBase&lt; Derived &gt; &amp;src, const MatrixBase&lt; OtherDerived &gt; &amp;dst, bool with_scaling=true)</div><div class="ttdoc">Returns the transformation between two point sets.</div><div class="ttdef"><b>Definition:</b> Umeyama.h:97</div></div>
<div class="ttc" id="agroup__enums_html_ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62"><div class="ttname"><a href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a0103672ae41005ab03b4176c765afd62">Eigen::ColMajor</a></div><div class="ttdeci">@ ColMajor</div><div class="ttdef"><b>Definition:</b> Constants.h:321</div></div>
<div class="ttc" id="agroup__enums_html_ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f"><div class="ttname"><a href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13a77c993a8d9f6efe5c1159fb2ab07dd4f">Eigen::RowMajor</a></div><div class="ttdeci">@ RowMajor</div><div class="ttdef"><b>Definition:</b> Constants.h:323</div></div>
<div class="ttc" id="agroup__enums_html_ggaacded1a18ae58b0f554751f6cdf9eb13ad0e7f67d40bcde3d41c12849b16ce6ea"><div class="ttname"><a href="group__enums.html#ggaacded1a18ae58b0f554751f6cdf9eb13ad0e7f67d40bcde3d41c12849b16ce6ea">Eigen::AutoAlign</a></div><div class="ttdeci">@ AutoAlign</div><div class="ttdef"><b>Definition:</b> Constants.h:325</div></div>
<div class="ttc" id="agroup__flags_html_gae4f56c2a60bbe4bd2e44c5b19cbe8762"><div class="ttname"><a href="group__flags.html#gae4f56c2a60bbe4bd2e44c5b19cbe8762">Eigen::RowMajorBit</a></div><div class="ttdeci">const unsigned int RowMajorBit</div><div class="ttdef"><b>Definition:</b> Constants.h:68</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition:</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition:</b> Meta.h:59</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition:</b> Constants.h:24</div></div>
<div class="ttc" id="astructEigen_1_1NumTraits_html"><div class="ttname"><a href="structEigen_1_1NumTraits.html">Eigen::NumTraits</a></div><div class="ttdoc">Holds information about the various numeric (i.e. scalar) types allowed by Eigen.</div><div class="ttdef"><b>Definition:</b> NumTraits.h:231</div></div>
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